Mayor Bloomberg disclosed yesterday that he met recently with Facebook founder Mark Zuckerberg to discuss the possibility of creating a page for the city on the enormously popular social networking site.

“I’m optimistic he’ll make some of his facilities available,” said the mayor. “This is the way we’re going. We just want to make sure we lead it rather than miss the opportunity to get some benefit out of it.”

Bloomberg, who has taken to carrying an iPad wherever he goes, wasn’t clear on what might emerge from the hookup.

“I’m not sure there’s anything Facebook can do for us,” he conceded at one point.

Bloomberg said the person who will have to determine that is Rachel Sterne, 27, the city’s new chief digital officer.

Sterne is working on a plan to increase the city’s presence on social-networking sites and other Internet access points. Her report should be out in just under three months.

In his State of the City speech, Bloomberg said he would make greater efforts to seek out citizen feedback — also known as crowdsourcing in the world of social media like Facebook — to get a better handle on the needs of the city’s residents.

Bloomberg’s affinity for Facebook is a switch from his skepticism just a few months ago. Back in October, during his weekly radio show, the topic of Facebook and Twitter users came up for discussion.

“Where do they get the time to do it?” Bloomberg asked. “Shouldn’t, aren’t — there have got to be other things in life to do.”

The mayor recalled looking at a friend’s Twitter account, only to find not much there.

The mayor’s opinion may have changed after he gave a speech on technological innovation at Facebook’s headquarters in Palo Alto, Calif. — where he pronounced himself mayor of the social-networking site on his Facebook page, which boasted roughly 27,000 followers at the time.

And yesterday, after the topic of Facebook linking up with the city came up, the mayor proclaimed, “There’s a lot of potential there.”